\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[scale=3]
\clip (-0.6,-0.2) rectangle (0.6,1.51);
\draw[step=.5cm,help lines] (-1.4,-1.4) grid (1.4,1.4);
\filldraw[fill=green!20,draw=green!50!black]
(0,0) -- (3mm,0mm) arc (0:30:3mm) -- cycle;
\draw[->] (-1.5,0) -- (1.5,0); \draw[->] (0,-1.5) -- (0,1.5);
\draw (0,0) circle (1cm);
\foreach \x/\xtext in {-1, -0.5/-\frac{1}{2}, 1}
\draw (\x cm,1pt) -- (\x cm,-1pt) node[anchor=north] {$\xtext$};
\foreach \y/\ytext in {-1, -0.5/-\frac{1}{2}, 0.5/\frac{1}{2}, 1}
\draw (1pt,\y cm) -- (-1pt,\y cm) node[anchor=east] {$\ytext$};
\end{tikzpicture}
\end{document}
